Two-Tailed Averaging improves generalization by optimizing the number of leading iterates to ignore.
problem Improving generalization in stochastic optimization with limited resources and hyperparameters.
method An anytime adaptive algorithm that balances the number of leading iterates to ignore for better generalization.
result Approximates the optimal tail at all optimization steps, improving generalization without hyperparameters.
Tail averaging consists in averaging the last examples in a stream. Common techniques either have a memory requirement which grows with the number of samples to average, are not available at every timestep or do not accomodate growing windows. We propose two techniques with a low constant memory cost that perform tail …
Improved TD learning with tail averaging and regularization achieves optimal convergence rates.
problem Convergence analysis of TD learning with linear function approximation.
method Tail-averaging and regularization applied to TD learning algorithm.
result Achieves optimal O(1/t) convergence rate in expectation and with high probability. New class of heavy-tailed distributions shows weighted averages dominate individual variables.
problem Understanding and comparing risks in heavy-tailed distributions.
method Introducing a new class of heavy-tailed distributions and proving stochastic dominance relations.
result Weighted averages of random variables in this class are stochastically larger than individual variables.
While stochastic gradient descent (SGD) is one of the major workhorses in machine learning, the learning properties of many practically used variants are poorly understood. In this paper, we consider least squares learning in a nonparametric setting and contribute to filling this gap by focusing on the effect and inter…
Paper provides tail bounds for stochastic mirror descent in heavy-tailed noise.
problem Optimizing convex and Lipschitz functions with heavy-tailed noise.
method Develops tail bounds for optimization error of Stochastic Mirror Descent.
result Tail bounds extend to heavier-tailed noise regimes without diameter constraints.
New measures capture tail dependence and non-exchangeability in financial data.
problem Underestimation of tail dependence and inability to capture non-exchangeable tail dependence.
method Tail copulas and novel tail dependence measures (MTCM, ATCM) are proposed.
result Captures non-exchangeable tail dependence and provides analytical forms for various copulas.
In a recent Nature paper, Gabaix et al. \cite{Gabaix03} presented a theory to explain the power law tail of price fluctuations. The main points of their theory are that volume fluctuations, which have a power law tail with exponent roughly -1.5, are modulated by the average market impact function, which describes the r…
DSI improves tail-risk estimation in generative models by averaging checkpoints.
problem Generative models' instability in rare adverse scenarios.
method Diachronic Sample Integration (DSI) ensembles generated samples across checkpoints.
result DSI reduces tail-estimation error compared to single-checkpoint baselines.
New method assesses financial and cyber risks under uncertainty.
problem Uncertainty in risk assessment for financial and cyber systems.
method Combines stochastic approximation and distorted mix method to compute worst case average value at risk.
result Efficient algorithm for tail uncertainty in multivariate distributions.
Boosted CVaR Classification improves tail performance in classification tasks.
problem Maximizing tail performance in classification tasks.
method Proposed Boosted CVaR Classification framework using randomized classifiers and LPBoost algorithm.
result Minimizing CVaR loss over randomized classifiers leads to better tail performance.
Improved tail risk forecasting model for assets using CAViaR with spillover effects.
problem Improving tail risk forecasting across assets.
method Component-based CAViaR model with spillover effects, decomposing risk into proper and spillover components.
result Spillover effects significantly improve out-of-sample tail risk forecasts.
We examine the performance of six estimators of the power-law cross-correlations -- the detrended cross-correlation analysis, the detrending moving-average cross-correlation analysis, the height cross-correlation analysis, the averaged periodogram estimator, the cross-periodogram estimator and the local cross-Whittle e…
New method approximates CVaR with less data for heavy-tailed risks.
problem Lack of data for accurate CVaR approximation in heavy-tailed distributions.
method Importance sampling based extrapolation for heavy-tailed distributions.
result Statistically consistent approximations with reduced data requirements.
Study on SA with heavy-tailed and LRD noise, establishing finite-time bounds.
problem Analyzing stochastic approximation under heavy-tailed and LRD noise.
method Noise-averaging argument to regularize impact of non-classical noise.
result Established first finite-time moment bounds for SA under heavy-tailed and LRD noise.
The paper establishes CLTs for Markov chains and improves sampling algorithms for heavy-tailed distributions.
problem Establishing central limit theorems for ergodic averages of Markov chains.
method Drift conditions to provide necessary and sufficient conditions for CLTs, including lower bounds on convergence rates.
result Sharp conditions and convergence rates for various MCMC algorithms on heavy-tailed targets.
New method estimates extreme outcomes in heavy-tailed data, breaking circular dependence.
problem Estimating outcomes for extreme events in heavy-tailed data.
method Proposes an ADRF estimator that includes a structured tail-shape output and a diagnostic to evaluate tail shape.
result Successfully reduces MAE in deep-tail and conditional-shortfall predictions.
Interpolating models can have heavy-tailed risk, leading to rare but severe errors.
problem Interpolating models' tail risk is poorly understood, affecting rare but impactful errors.
method Large-deviation methods to study the fragility of high-dimensional linear interpolators.
result Ridgeless regression exhibits heavy-tailed risk, while ridge-regularized estimators have better tail behavior.
A new method forecasts financial tail risks by combining and weighting quantiles.
problem Reducing uncertainty in financial tail risk forecasting.
method Two-step procedure: quantile combination followed by ES computation.
result The proposed framework outperforms individual models and simple approaches.
New study shows diversification can increase risk for heavy-tailed losses.
problem Diversification can increase tail risk for heavy-tailed losses.
method Comparison of diversified portfolio to a 'one-basket' benchmark.
result Diversified portfolio has larger tail probabilities than a 'one-basket' benchmark for all thresholds.
A new method improves posterior approximation for complex distributions.
problem Difficulty in capturing multimodal and heavy-tailed posteriors with standard normalizing flows.
method StiCTAF: stick-breaking mixture base with component-wise tail adaptation.
result Improved tail recovery and better mode coverage compared to benchmarks.
A federated learning framework using superquantile aggregation for robust performance across heterogeneous data.
problem Robust predictive performance across clients with heterogeneous data.
method Superquantile-based learning objective and stochastic training algorithm with differential privacy.
result Proves finite time convergence guarantees and demonstrates competitive performance with tail statistics improvement.
New convergence rates for SGD under heavy-tailed noise with infinite variance.
problem Convergence analysis of SGD under heavy-tailed noise with infinite variance.
method Identifying a condition on the Hessian and providing a convergence rate for the distance to the global optimum.
result SGD can converge to the global optimum under heavy-tailed noise with infinite variance.
Model predicts methane emissions from oil sands tailing ponds, suggesting significant environmental impact.
problem Estimating methane emissions from inactive oil sands tailing ponds.
method Physics constrained machine learning model using real-time weather data and laboratory experiments.
result Active oil sands tailing ponds emit between 950 to 1500 tonnes of methane per year, equivalent to 6000 gasoline vehicles.
Model monthly VIX and stock returns using log-Heston model.
problem Modeling monthly VIX and stock index returns accurately.
method Log-Heston model applied to logarithm of VIX as an autoregression, normalizing stock returns by VIX.
result Model captures independent, identically distributed Gaussian stock returns after normalization.
Unlike human speakers, typical text-to-speech (TTS) systems are unable to produce multiple distinct renditions of a given sentence. This has previously been addressed by adding explicit external control. In contrast, generative models are able to capture a distribution over multiple renditions and thus produce varied r…
New method bounds stochastic subgradient methods with heavy-tailed noise.
problem Bounding stochastic subgradient methods under heavy-tailed noise.
method Clipped version of projected stochastic subgradient method.
result Near optimal any-time and finite horizon bounds for averaging schemes.
This study uses local Gaussian correlation to analyze stock return tails, revealing more sensitive network properties.
problem Misleading results from Pearson correlation in financial networks.
method Local Gaussian correlation coefficient for capturing nonlinear dependence and heavy-tailed distributions.
result Local Gaussian correlation network among negative tails is more sensitive to stock market risks.
Investment strategy for DC pension plan with inflation risk and tail VaR constraint.
problem Maximizing terminal wealth for pension member with tail VaR constraint.
method Lagrange method and quantile optimization techniques.
result Optimal investment strategy and output in closed-form derived.
We analyze the statistical dependency structure of the S&P 500 constituents in the 4-year period from 2007 to 2010 using intraday data from the New York Stock Exchange's TAQ database. With a copula-based approach, we find that the statistical dependencies are very strong in the tails of the marginal distributions. This…
Bayesian VAR and Elliptical Black-Litterman models improve portfolio optimization during regime changes and heavy-tailed returns.
problem Portfolio optimization under market regime changes and heavy-tailed returns.
method BAVAR-BLED algorithm combining BAVAR and Black-Litterman models with Elliptical Distributions.
result Significant outperformance of state-of-the-art methods in Sharpe, Sortino ratios, and total returns.
A new algorithm reduces regret in cooperative multi-agent bandits with heavy-tailed data.
problem Cooperative multi-agent bandits with heavy-tailed data.
method MP-UCB algorithm incorporating robust estimation with message-passing protocol.
result Optimal regret bounds for MP-UCB in various settings.
The paper proposes a new method to measure risk with fine-grained tail sensitivity.
problem Risk measures that do not account for tail sensitivity are insufficient for machine learning systems.
method The approach involves specifying a reference distribution with desired tail behavior and constructing risk measures compatible with this upper probability.
result Risk measures with fine-grained tail sensitivity can replace the expectation operator in machine learning systems.
New methods solve optimization problems with heavy-tailed noise, improving upon existing complexity bounds.
problem Optimization problems with heavy-tailed noise and weakly average smoothness.
method Normalized stochastic first-order methods with Polyak, multi-extrapolated, and recursive momentum.
result First-order oracle complexity results for finding approximate stochastic stationary points under heavy-tailed noise.
We extend the model of rational bubbles of Blanchard and of Blanchard and Watson to arbitrary dimensions d: a number d of market time series are made linearly interdependent via d times d stochastic coupling coefficients. We first show that the no-arbitrage condition imposes that the non-diagonal impacts of any asset i…
In this paper, we show how the sampling properties of the Hurst exponent methods of estimation change with the presence of heavy tails. We run extensive Monte Carlo simulations to find out how rescaled range analysis (R/S), multifractal detrended fluctuation analysis (MF-DFA), detrending moving average (DMA) and genera…
New conformal prediction methods for long-tailed classification problems.
problem Rare classes are systematically omitted in existing conformal prediction methods.
method Introduced a new conformal score function and a new interpolation procedure.
result Smoothly trade off set size and class-conditional coverage.
We have analyzed the statistical probabilities of limit-order book (LOB) shape through building the book using the ultra-high-frequency data from 23 liquid stocks traded on the Shenzhen Stock Exchange in 2003. We find that the averaged LOB shape has a maximum away from the same best price for both buy and sell LOBs. Th…
This work analyzes CVaR under heavy-tailed data, providing generalization and robustness bounds.
problem Understanding CVaR's behavior under heavy-tailed data and rare high-impact losses.
method Learning-theoretic analysis of CVaR-based empirical risk minimization.
result Sharp, high-probability generalization and excess risk bounds under minimal moment assumptions.
SGD in linear regression overfits but performs well due to bias-variance trade-off.
problem Understanding overfitting in SGD for linear regression.
method Constant-stepsize SGD with iterate averaging or tail averaging, analyzing full eigenspectrum of data covariance matrix.
result Sharp excess risk bounds revealing bias-variance decomposition for SGD in linear regression.
The paper optimizes portfolios using relative tail risk measures.
problem Optimizing portfolios with respect to relative tail risk.
method Analytic forms of portfolio CoVaR and CoCVaR derived on a market model. Monte-Carlo simulation for CoCVaR and marginal contributions. Risk budgeting method applied.
result Derivation of analytic forms for CoVaR and CoCVaR, and their marginal contributions.
Adaptive estimation for nonstationary time series reduces computational cost.
problem Estimating parameters of nonstationary time series with varying parameters over time.
method Moving exponential moving ML estimator for scale parameter estimation.
result Significantly improved log-likelihoods compared to standard estimation.
Maximal concentration bounds for stochastic approximation with heavy-tailed noise.
problem Analyzing the convergence of stochastic approximation algorithms under heavy-tailed Markovian noise.
method Novel Lyapunov function and black-box truncation argument.
result Tail behavior of the error can be sub-Gaussian, sub-Weibull, or lighter than any Pareto but heavier than any Weibull.
SHIFT improves robustness in estimating dose-response functions with heavy-tailed contamination.
problem Outliers bias estimates of average dose-response functions in heavy-tailed data.
method SHIFT combines cross-fit nuisance orthogonalization, Welsch-loss, and defensive OLS refit.
result SHIFT reduces RMSE from 1.03 to 0.33 on localized contamination test.
Proposes a new framework to manage venture capital portfolio risk by focusing on deal-level correlations.
problem Managing venture capital portfolio risk, especially extreme outcomes.
method Gaussian-copula-based framework that learns deal-level dependence from observed joint success frequencies.
result Correlation amplifies extreme upside outcomes, shifting portfolio distribution toward heavier right tails.
Given two or more Deep Neural Networks (DNNs) with the same or similar architectures, and trained on the same dataset, but trained with different solvers, parameters, hyper-parameters, regularization, etc., can we predict which DNN will have the best test accuracy, and can we do so without peeking at the test data? In …
This work creates a CS for non-negative heavy-tailed data with bounded mean.
problem Constructing a confidence sequence for non-negative heavy-tailed data with bounded mean.
method Non-parametric, non-asymptotic lower confidence sequence construction.
result The constructed CS is efficient and can be converted into a closed-interval CS.
The paper explains how importance sampling can be used for optimization of rare events.
problem Minimizing tail risks in stochastic optimization formulations.
method Importance sampling for reducing sample requirements in estimating rare events.
result Effective importance sampling techniques for optimization of rare events.